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Showing 1 to 8 of 8 for “"Automorphic representations"”.
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Fields of rationality of cuspidal automorphic representations
… the growth of fields of rationality of cuspidal automorphic representations in families. Specifically, if F is a family of cuspidal automorphic representations with fixed central character, prescribed behavior at the Archimedean places, and such that the finite component [pi] [infinity] has a …
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Level raising for automorphic representations of GL(2n)
… regular algebraic, conjugate self-dual, cuspidal automorphic representation $\Pi$ of $\mathrm{GL}(N)$ over a CM number field $E$ (or, more generally, to a regular algebraic isobaric sum of conjugate self-dual, cuspidal representations), we can attach a continuous $\ell$-adic Galois representation …
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An ordinary rank-two case of local-global compatibility for automorphic representations of arbitrary weight over CM fields
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms
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p-arithmetic cohomology and p-adic automorphic forms
… group with coefficients in finite-dimensional representations can be described in terms of automorphic representations of the group. In this thesis, we prove similar results for the cohomology of an *S*-arithmetic groups (where *S* is a finite set of primes) with coefficients in different types …
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Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions
A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by …
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First explicit reciprocity law for unitary Friedberg—Jacquet periods
… on constructing such systems for other Galois representations, including settings such as twisted and cubic triple product, symmetric cube, and Rankin--Selberg, with applications to the Bloch--Kato conjecture and to Iwasawa theory. This thesis studies the case of Galois representations attached …
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Arithmetic inner product formula for unitary groups
… central derivatives of L-functions of cuspidal automorphic representations for unitary groups of even variables defined over a totally real number field, and their relation with the canonical height of special cycles on Shimura varieties attached to unitary groups of the same size. We formulate …
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Character Theory and Artin L-functions
In the spirit of Artin, Brauer, and Heilbronn, we implement representation theory together with the Artin formalism to study L-functions in this thesis. One of the major themes is motivated by the work of Heilbronn and many others on classical Heilbronn characters. We define the arithmetic …